A Brief Introduction to Mathematica

Windows Notebook Interface:

If you are using Mathematica on a Mac, in PC Windows, or the X Windows System under UNIX, you can start Mathematica by double clicking on the Mathematica icon. A blank notebook page will be opened into which you can enter your Mathematica commands. To execute the commands you have entered, press shift-Enter; if you are using this interface, you should interpret "enter" in the text which follows as meaning "press shift-enter". File, Edit, Cell, Graph, Action, Style, Options, Window, and Help menus are available at the top of the screen to assist you in performing operations within Mathematica.

Command line interface:

To start Mathematica, enter math at the system prompt. After the Mathematica kernel loads, the "IN[1]:=" prompt will appear indicating that Mathematica has started and is waiting for you to enter commands.

SYNTAX

Mathematica is case sensitive (e.g., "a" is different from "A"). Mathematica built-in commands and functions begin with capital letters. It is recommended that you use all lower case letters for names of variables and functions you define. Alternatively in graphical environments, you can use symbols to represent variables in your Mathematica expressions by selecting the character from the Palettes submenu of the File menu or by entering a keyboard equivalent of the symbol, e.g., enter \[Beta] or Esc-b-Esc to obtain the character beta.

Parentheses are used to indicate grouping of terms.

Spaces between numbers or variable names indicate multiplication; other spaces can be added for readability between numbers, variables, and functions, but are not required. Use parentheses to specify the order of calculations, otherwise the default order of mathematical precedence is:

     Raise to a power        x^2   e.g.,  250000 is 2.5 10^5
     Negation                 -x
     Divide                  x/y
     Multiply                x y    or    x*y   or    x * y
     Addition                x+y

Note: a number preceding a variable name indicates that the variable is to be multiplied by that number, e.g., 3x indicates that the value assigned to x is to be multiplied by 3.

Square braces ( [ and ] ) are used to enclose arguments of Mathematica functions. Double square brackets are used for indexing, e.g., x[[i]]

Curly braces ( { and} ) are used for lists, e.g., {x,y,z}. Arrays are represented as "lists of lists", e.g. {{1,2,3},{4,5,6}}

To reduce typing, use the percent (%) symbol to represent the last result.

Multiple Mathematica statements can be included on the same line by separating statements from one another with semicolons, e.g.: x=4; y=6; w=7; z=x*y+w

To suppress the output display, include a semicolon at the end of a line, e.g., a=b=0;

USAGE

You can now type in Mathematica commands or equations. For example if you enter "2*3+5" as the first command, the "Out[1]=" response will display the value 11 as the result of this computation.

You can assign a value to a variable by entering the variable name followed by an equal sign and a numeric value or function, e.g., "a = 2*3+5" or "z = x / y".

A value may be assigned to more than one variable by a single statement, e.g., to assign zero to a, b, and c, enter: a=b=c=0

If you enter the name of a defined variable at the Mathematica prompt, it will display the value assigned to the variable. Assuming all variables within it have been defined and an exact result can be computed, entering a function or the name of a variable to which a function has been assigned, will result in the display of the computed result of the function, e.g., 2 will be displayed when Log[10,100] is entered. If an exact result cannot be computed, Mathematica will simply redisplay the function, e.g., Log[10] will be displayed when Log[10] is entered.

Note: To display an approximate (typically 6 digits of precision) numeric evaluation of a non-exact function, enclose the function in square brackets and precede it by a capital N, e.g., N[Log[10]]

To change the precision of the displayed result, include a comma and the number of digits within the square brackets after the function to be evaluated, e.g., N[Log[10],12]

To remove a definition assigned to a variable or function, enter: x=. or Clear[x], where "x" is the name of the variable or function you which to deassign. It is recommended that one deassign variables once you no longer need them.

Mathematica supports a variety of Mathematical operations, e.g., use Solve to obtain the solution to equations or Integrate to perform integration. A variety of graphics capabilities are also included within Mathematica through the Plot or Plot3D commands.

HELP

If you are using a Windows based environment, you can obtain assistance using the Help menu included at the top of the Mathematica window.

Internal help can be obtained using a question mark. For help with the function Log, enter: ?Sqrt

To display extended help about a topic, precede the name with two questions marks, e.g., ??Sqrt

To obtain a listing of all commands and functions beginning with the letter S, enter: ?S*

SAVING Stored Values

The Save Command can be used to save values of variables and functions to a file. For example, to save previous definitions of x and y in the file "filename", enter: Save["filename",x,y]

You can retrieve values saved in "filename" by entering: <<filename

SYSTEM COMMANDS Within Mathematica

To issue a command to the operating system from within the Mathematica environment, precede the system command with an exclamation point (!), e.g., in the UNIX environment, to issue the ls command to list files in the current directory, enter: !ls

EXITing from Mathematica

To interrupt a command in progress, try entering Control-C or Command-. Note that it may take some time for the Mathematica kermel to interrupt the process.

To exit from Mathematica, select Exit from the File menu of a Windows based environment; in command line environments, enter Quit or press Ctrl-D.